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1.     (Binomial Distribution)Telephone manufacturers now offer 1000 different choices for a telephone (as combinations of color, type, options, portability, etc.). A company is opening a large regional office, and each of its 200 managers is allowed to order his or her own choice of a telephone. Assuming independence of choices and that each of the 1000 choices is equally likely, what is the probability that a particular choice will be made by none, one, two, or three of the managers?

You pick a card from a deck. If it is a face card, you will win 500. If you get an ace, you will win 1000. If the card you picked is red you get 100. For any other card, you will win nothing. Find the expected value that you can possibly win

Solve the ff linear programming graphically method maximize Z= 30×, + 100×² 4×,+6×²≤ 90 8×, +6×, ≤100 5×,+4×,≤ 80 ×, ×, ≥ 0

Find Larange’s interpolating polynomial passing through set of points

(0,2) (2,-2),(3,-1),Use it to find

at x = 2

1.Consider the equation xe^x = cos x

(a) Apply the intermediate value theorem to show that the function has a root in the interval

[0, 1].

(b) Find the real root using the secant method. Start with the two points, x1 = 0 and x2 = 1

and carry out the first four iterations.

(c) Find the real root using the Newton-Raphson method. Start with an initial approximation,

x0 = 0.5 correct to two decimal places.

2.Consider the initial value problem

dy = t(y + t) − 2, y(0) = 2. It is derivative of y respect to t

dt

(a) Use Eulers method with step sizes h = 0.3, h = 0.2 and h = 0.15, compute the approximations to y(0.6).

(b) Use the fourth order Runge-Kutta method Compute y(0.4) with h = 0.2.

Find a root of the equation cos x- e^x=0 correct to three decimal places in the

interval (0,1) after four iterations by Secant method

Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following: a. f (8.4) if f (8.1) = 16.94410, f (8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091 b. f  −1 3  if f (−0.75) = −0.07181250, f (−0.5) = −0.02475000, f (−0.25) = 0.33493750, f (0) = 1.10100000 c. f (0.25) if f (0.1) = 0.62049958, f (0.2) = −0.28398668, f (0.3) = 0.00660095, f (0.4) = 0.24842440 d. f (0.9) if f (0.6) = −0.17694460, f (0.7) = 0.01375227, f (0.8) = 0.22363362, f (1.0) = 0.65809197

Using sin( )1.0 = .0 09983 and sin( )2.0 = .0 19867 , find an approximate value of

sin( 15.0 ) by using Lagrange interpolation. Obtain a bound on the truncation error.

A travel agency conducted a survey to find the mode of transport perceived to be the “safest” among their customers. The results showed that 45% of respondents perceive that air planes are the safest. Develop a 95% confidence interval for the proportion of people who think airplane is the safest mode of transportation.

Find a real root of the equation 3x + sinx − e

x = 0 by the method of

bisection, correct to two decimal places.

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